4,5&6 questions

Homework #2

The first three problems are designed to be completed by hand:

1. In many areas, newspaper carriers deliver newspapers via automobile due to the length of

the routes. In a random sample of 28 newspaper carriers using an automobile, the sample

mean route length was 16.7 miles, and the sample standard deviation was 3.4 miles. If we

assume the route length is reasonably normally distributed, find the 95% confidence

interval for the true mean route length for newspaper carriers who use their automobile to

deliver newspapers?

2. Residential mailboxes in Des Moines, IA should be installed so that the bottom of the

mailbox is 42 inches above the ground. A random sample of 75 mailboxes was selected

and the height of each mailbox was measured, resulting in a sample mean of 43.22 inches

and a sample standard deviation of 7.6 inches. Is there evidence to suggest that the

mailboxes in Des Moines, IA are not being installed as required? Test by calculating a p-

value, with a significance level α = 0.05.

3. A 42-inch large screen plasma TV is required to consume no more than 350 Watts of power

in order to receive Energy Star certification. A random sample of 7 TVs which had received

the Energy Star certification was selected and their power consumption was measured. The

sample mean was 353.8 Watts and the sample standard deviation was 5.6 Watts. Is there

evidence that the TVs are not meeting the Energy Star certification? Test using a

significance level of α = 0.05, and you can assume the distribution is reasonably normal.

The remaining problems are to be completed using Excel and SAS. The dataset is posted to

Blackboard in a single Excel file, with three tabs, labeled Dataset #1, Dataset #2, and Dataset

#3.

Problem 4:

Dataset #1 contains data pairs represent cost of living index for grocery items and health care

for 45 different metropolitan areas. Reference: Statistical Abstract of the United States, 120th

edition.

Does this data suggest that the cost of health care exceeds the cost of grocery items? Conduct

your test by calculating a p-value and testing at a significance level of α = 0.05. This analysis

should be conducted using Excel and SAS. You need to justify any assumptions (e.g.,

approximate normality) that you need to make in order to conduct your hypothesis test.

Problem 5:

Dataset #2 contains the glucose blood level (mg/100ml) after a 12 hour fast for a random

sample of 70 women. Reference: American J. Clin. Nutr. Vol. 19, 345-351.

1) Descriptive Analysis of the Dataset:

a. Produce a histogram of the dataset.

b. Produce a stem and leaf diagram for the dataset.

c. Produce a boxplot of the dataset.

d. Produce a normal probability plot of the dataset.

2) Initial Analysis of the Dataset. Based on the above:

a. Identify and list any outliers in the dataset.

b. Assess the normality of the dataset and justify your assessment.

3) Descriptive Analysis without outliers. Remove any outliers identified by your above

analysis, and, using your revised dataset with the outliers removed:

a. Produce a histogram of the revised dataset.

b. Produce a stem and leaf diagram for the revised dataset.

c. Produce a boxplot of the revised dataset.

d. Produce a probability plot of the revised dataset.

4) Analysis of the Dataset without outliers. Based on the descriptive analysis conducted

above:

a. Verify that all outliers were removed.

b. Assess the normality of the revised dataset. Comment on any changes in your

assessment of normality.

Problem 6:

For this problem, you will analyze Dataset #3. No source information is provided for this

dataset as it was generated by your instructor.

1) Descriptive Analysis of the Dataset:

a. Produce a histogram of the dataset.

b. Produce a stem and leaf diagram for the dataset.

c. Produce a boxplot of the dataset.

d. Produce a normal probability plot of the dataset.

Based on the descriptive analysis conducted above:

2) Identify and list any outliers in the dataset.

3) Is the dataset skewed or symmetric? If you determine it is skewed, what direction is the

skew?

4) Assess the normality of the dataset and justify your assessment.

5) What distribution do you believe best fits this dataset? Justify your response based on

the analysis conducted above.